I see/hear this question quite a bit, so it’s worth an answer.
The question is: When I get a Microsoft Band replaced, does the original warranty transfer, or does the new Band come with a new warranty?
Answer: According to the Microsoft warranty documents (HERE)…
After repair or replacement, Your Microsoft Band or Accessory will be covered by this warranty for the longer of the remainder of Your original Warranty Period, or 90 days after Microsoft or the reseller ships it to You.
To put it simply, your original warranty does, indeed, transfer. If you have 6 months left of your original warranty, the replacement Band comes with a 6-month warranty. However, if your original warranty expires sooner than 90 days after being replaced, Microsoft will support the replacement under warranty for a full 90 days.